A165155 a(n) = 100*a(n-1) + 11^(n-1) for n>0, a(0)=0.

0, 1, 111, 11221, 1123431, 112357741, 11235935151, 1123595286661, 112359548153271, 11235955029685981, 1123595505326545791, 112359550558592003701, 11235955056144512040711, 1123595505617589632447821, 112359550561793485956926031, 11235955056179728345526186341

Offset: 0

Author

Mark Dols, Sep 05 2009

Keywords

• nonn
• easy

Comments

Generalization of A000225. - Mark Dols, Jan 28 2010

Examples

			From _Mark Dols_, Jan 28 2010: (Start)
As triangle:
  ........... 1
  ......... 1 1 1
  ....... 1 1 2 2 1
  ..... 1 1 2 3 4 3 1
  ... 1 1 2 3 5 7 7 4 1
  . 1 1 2 3 5 9 3 5 1 5 1
  1 1 2 3 5 9 5 2 8 6 6 6 1
(Mirrored version of A162741) (End)
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..495
• Index entries for linear recurrences with constant coefficients, signature (111,-1100).

Crossrefs

Cf. A000225, A021093, A094704, A162741, A164913.

Programs

Magma

[(1/89)*(100^n-11^n): n in [0..40]] // Vincenzo Librandi, Dec 05 2010

Mathematica

RecurrenceTable[{a[0]==0,a[n]==100a[n-1]+11^(n-1)},a,{n,40}] (* Harvey P. Dale, Feb 20 2016 *)

SageMath

[(10^(2*n) - 11^n)/89 for n in range(41)] # G. C. Greubel, Feb 09 2023

Formula

G.f.: x/((1-11*x)*(1-100*x)). - R. J. Mathar, Nov 02 2016

E.g.f.: (1/89)*(exp(100*x) - exp(11*x)). - G. C. Greubel, Feb 09 2023

Extensions

a(0) prepended by Bruno Berselli, Oct 02 2015